This proposal addresses itself to three distinct areas of research: (1) modelling as it pertains to epidemic processes; (2) estimation within the content of analysing epidemic data, as well as estimation of Markov chains in general; and (3) sequential analysis with emphasis on the development of optimum tests for two-sided alternative hypotheses. While the immediate concern in (1) is with epidemic models, the mathematics to be developed will also be widely applicable to many other stochastic processes. The work on estimation procedures will be concerned largely with maximum likelihood, empirical Bayes and time series methods. The applicability of this work will venture well beyond the area of epidemics which originally motivated the research. Finally, the sequential tests to be developed will attempt to combine the essential features of Wald's sequential probability ratio tests and diffusion processes.